Interference in Thin Films, Interference in Thin Films, finalfinal

An example of An example of different indices different indices of refractionof refraction

A coating on a A coating on a solar cellsolar cell

Problem Solving with Thin Films, 3

Equation1 phase reversal

0 or 2 phase reversals

2nt = (m + ½) constructive destructive

2nt = m destructive constructive

Problem Solving Strategy Problem Solving Strategy with Thin Films, 1with Thin Films, 1

Identify the thin film causing the Identify the thin film causing the interferenceinterference

The type of interference – The type of interference – constructive or destructive – that constructive or destructive – that occurs is determined by the phase occurs is determined by the phase relationship between the upper relationship between the upper and lower surfacesand lower surfaces

Problem Solving with Thin Problem Solving with Thin Films, 2Films, 2

Phase differences have two causesPhase differences have two causes differences in the distances traveleddifferences in the distances traveled phase changes occurring on reflectionphase changes occurring on reflection Both must be considered when determining Both must be considered when determining

constructive or destructive interferenceconstructive or destructive interference The interference is constructive if the path The interference is constructive if the path

difference is an integral multiple of difference is an integral multiple of λ and λ and destructive if the path difference is an odd destructive if the path difference is an odd half multiple of λhalf multiple of λ The conditions are reversed if one of the waves The conditions are reversed if one of the waves

undergoes a phase change on reflectionundergoes a phase change on reflection

DiffractionDiffraction Huygen’s principle Huygen’s principle

requires that the requires that the waves spread out after waves spread out after they pass through slitsthey pass through slits

This spreading out of This spreading out of light from its initial line light from its initial line of travel is called of travel is called diffractiondiffraction In general, diffraction In general, diffraction

occurs when wave pass occurs when wave pass through small openings, through small openings, around obstacles or by around obstacles or by sharp edgessharp edges

Diffraction, 2Diffraction, 2

A single slit placed between a distant A single slit placed between a distant light source and a screen produces a light source and a screen produces a diffraction patterndiffraction pattern It will have a broad, intense central bandIt will have a broad, intense central band The central band will be flanked by a The central band will be flanked by a

series of narrower, less intense series of narrower, less intense secondary bandssecondary bands

Called secondary maximaCalled secondary maxima The central band will also be flanked by The central band will also be flanked by

a series of dark bandsa series of dark bands Called minimaCalled minima

Diffraction, 3Diffraction, 3

The results of the single slit cannot The results of the single slit cannot be explained by geometric opticsbe explained by geometric optics Geometric optics would say that light Geometric optics would say that light

rays traveling in straight lines should rays traveling in straight lines should cast a sharp image of the slit on the cast a sharp image of the slit on the screenscreen

Single Slit DiffractionSingle Slit Diffraction According to Huygen’s According to Huygen’s

principle, each portion principle, each portion of the slit acts as a of the slit acts as a source of wavessource of waves

The light from one The light from one portion of the slit can portion of the slit can interfere with light interfere with light from another portionfrom another portion

The resultant intensity The resultant intensity on the screen on the screen depends on the depends on the direction direction θθ

Single Slit Diffraction, 2Single Slit Diffraction, 2 All the waves that originate at the slit are in All the waves that originate at the slit are in

phasephase Wave 1 travels farther than wave 3 by an Wave 1 travels farther than wave 3 by an

amount equal to the path difference (a/2) sin amount equal to the path difference (a/2) sin θ θ

If this path difference is exactly half of a If this path difference is exactly half of a wavelength, the two waves cancel each other wavelength, the two waves cancel each other and destructive interference resultsand destructive interference results

In general, In general, destructive interferencedestructive interference occurs for occurs for a single slit of width a when sin a single slit of width a when sin θθdarkdark = mλ / a = mλ / a m = m = 1, 1, 2, 2, 3, …3, …

Single Slit Diffraction, 3Single Slit Diffraction, 3 The general features of The general features of

the intensity distribution the intensity distribution are shownare shown

A broad central bright A broad central bright fringe is flanked by fringe is flanked by much weaker bright much weaker bright fringes alternating with fringes alternating with dark fringesdark fringes

The points of The points of constructive interference constructive interference lie approximately lie approximately halfway between the halfway between the dark fringesdark fringes

QUICK QUIZ 24.1

In a single-slit diffraction experiment, as the width of the slit is made smaller, the width of the central maximum of the diffraction pattern becomes (a) smaller, (b) larger, or (c) remains the same.

QUICK QUIZ 24.1 ANSWER

(b). The outer edges of the central maximum occur where sin θ = ± λ/a. Thus, as a, the width of the slit, becomes smaller, the width of the central maximum will increase.

Diffraction GratingDiffraction Grating

The diffracting grating consists of The diffracting grating consists of many equally spaced parallel slitsmany equally spaced parallel slits A typical grating contains several A typical grating contains several

thousand lines per centimeterthousand lines per centimeter The intensity of the pattern on the The intensity of the pattern on the

screen is the result of the screen is the result of the combined effects of interference combined effects of interference and diffractionand diffraction

Diffraction Grating, contDiffraction Grating, cont The condition for The condition for

maximamaxima is is d sin d sin θθbrightbright = m λ = m λ

m = 0, 1, 2, …m = 0, 1, 2, … The integer m is the The integer m is the

order numberorder number of the of the diffraction patterndiffraction pattern

If the incident radiation If the incident radiation contains several contains several wavelengths, each wavelengths, each wavelength deviates wavelength deviates through a specific through a specific angleangle

Diffraction Grating, finalDiffraction Grating, final All the wavelengths are All the wavelengths are

focused at m = 0focused at m = 0 This is called the zeroth This is called the zeroth

order maximumorder maximum The first order maximum The first order maximum

corresponds to m = 1corresponds to m = 1 Note the sharpness of Note the sharpness of

the principle maxima and the principle maxima and the broad range of the the broad range of the dark areadark area This is in contrast to to This is in contrast to to

the broad, bright fringes the broad, bright fringes characteristic of the two-characteristic of the two-slit interference patternslit interference pattern

Polarization of Light Polarization of Light WavesWaves

Each atom produces Each atom produces a wave with its own a wave with its own orientation of Eorientation of E

All directions of the All directions of the electric field E vector electric field E vector are equally possible are equally possible and lie in a plane and lie in a plane perpendicular to the perpendicular to the direction of direction of propagationpropagation

This is an unpolarized This is an unpolarized wavewave

Polarization of Light, contPolarization of Light, cont A wave is said to be A wave is said to be linearly linearly

polarizedpolarized if the resultant if the resultant electric field vibrates in the electric field vibrates in the same direction at all times same direction at all times at a particular pointat a particular point

Polarization can be obtained Polarization can be obtained from an unpolarized beam from an unpolarized beam by by selective absorptionselective absorption reflectionreflection scatteringscattering

Polarization by Selective Polarization by Selective AbsorptionAbsorption

The most common technique for polarizing lightThe most common technique for polarizing light Uses a material that transmits waves whose Uses a material that transmits waves whose

electric field vectors in the plane parallel to a electric field vectors in the plane parallel to a certain direction and absorbs waves whose certain direction and absorbs waves whose electric field vectors are perpendicular to that electric field vectors are perpendicular to that directiondirection

Selective Absorption, contSelective Absorption, cont

E. H. Land discovered a material E. H. Land discovered a material that polarizes light through that polarizes light through selective absorptionselective absorption He called the material He called the material polaroidpolaroid The molecules readily absorb light The molecules readily absorb light

whose electric field vector is parallel to whose electric field vector is parallel to their lengths and transmit light whose their lengths and transmit light whose electric field vector is perpendicular to electric field vector is perpendicular to their lengthstheir lengths

Selective Absorption, finalSelective Absorption, final

The intensity of the polarized beam The intensity of the polarized beam transmitted through the second transmitted through the second polarizing sheet (the analyzer) varies polarizing sheet (the analyzer) varies asas I = II = Ioo cos cos22 θθ

IIoo is the intensity of the polarized wave is the intensity of the polarized wave incident on the analyzerincident on the analyzer

This is known as This is known as Malus’ LawMalus’ Law and applies to any and applies to any two polarizing materials whose transmission two polarizing materials whose transmission axes are at an angle of axes are at an angle of θ to each otherθ to each other

Polarization by ReflectionPolarization by Reflection When an unpolarized light beam is reflected When an unpolarized light beam is reflected

from a surface, the reflected light isfrom a surface, the reflected light is Completely polarizedCompletely polarized Partially polarizedPartially polarized UnpolarizedUnpolarized

It depends on the angle of incidenceIt depends on the angle of incidence If the angle is 0° or 90°, the reflected beam is If the angle is 0° or 90°, the reflected beam is

unpolarizedunpolarized For angles between this, there is some degree of For angles between this, there is some degree of

polarizationpolarization For one particular angle, the beam is completely For one particular angle, the beam is completely

polarizedpolarized

Polarization by Reflection, Polarization by Reflection, contcont

The angle of incidence for which the The angle of incidence for which the reflected beam is completely polarized is reflected beam is completely polarized is called the called the polarizing anglepolarizing angle, , θθpp

Brewster’s Law relates the polarizing Brewster’s Law relates the polarizing angle to the index of refraction for the angle to the index of refraction for the materialmaterial

θθpp may also be called Brewster’s Angle may also be called Brewster’s Angle

pp

p tancos

sinn

Polarization by ScatteringPolarization by Scattering

When light is incident on a system When light is incident on a system of particles, the electrons in the of particles, the electrons in the medium can absorb and reradiate medium can absorb and reradiate part of the lightpart of the light This process is called This process is called scatteringscattering

An example of scattering is the An example of scattering is the sunlight reaching an observer on sunlight reaching an observer on the earth becoming polarizedthe earth becoming polarized

Polarization by Scattering, Polarization by Scattering, contcont

The horizontal part of The horizontal part of the electric field the electric field vector in the incident vector in the incident wave causes the wave causes the charges to vibrate charges to vibrate horizontallyhorizontally

The vertical part of the The vertical part of the vector simultaneously vector simultaneously causes them to causes them to vibrate verticallyvibrate vertically

Horizontally and Horizontally and vertically polarized vertically polarized waves are emittedwaves are emitted